Abstract

A linear stability analysis of the planar one dimensional space charge limited flow is performed when the current is determined by a current-field relation, e.g., the Fowler-Nordheim or any other emission model. The initial velocity is assumed the same for all emitted electrons. The flow is shown to be stable with decaying oscillations depending on the nature of the emission law, including in some situations non-oscillating slowly decaying modes. When the emission variations are due only to changes of the initial flow velocity, the time of decay can be much longer than the electron transit time for a given flow setup.